comparison DEPENDENCIES/generic/include/boost/graph/isomorphism.hpp @ 16:2665513ce2d3

Add boost headers

+// Copyright (C) 2001 Jeremy Siek, Douglas Gregor, Brian Osman
+//
+// Distributed under the Boost Software License, Version 1.0. (See
+// accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+#ifndef BOOST_GRAPH_ISOMORPHISM_HPP
+#define BOOST_GRAPH_ISOMORPHISM_HPP
+
+#include <utility>
+#include <vector>
+#include <iterator>
+#include <algorithm>
+#include <boost/config.hpp>
+#include <boost/assert.hpp>
+#include <boost/smart_ptr.hpp>
+#include <boost/graph/depth_first_search.hpp>
+#include <boost/detail/algorithm.hpp>
+#include <boost/pending/indirect_cmp.hpp> // for make_indirect_pmap
+#include <boost/concept/assert.hpp>
+
+#ifndef BOOST_GRAPH_ITERATION_MACROS_HPP
+#define BOOST_ISO_INCLUDED_ITER_MACROS // local macro, see bottom of file
+#include <boost/graph/iteration_macros.hpp>
+#endif
+
+namespace boost {
+
+  namespace detail {
+
+    template <typename Graph1, typename Graph2, typename IsoMapping,
+      typename Invariant1, typename Invariant2,
+      typename IndexMap1, typename IndexMap2>
+    class isomorphism_algo
+    {
+      typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;
+      typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
+      typedef typename graph_traits<Graph1>::edge_descriptor edge1_t;
+      typedef typename graph_traits<Graph1>::vertices_size_type size_type;
+      typedef typename Invariant1::result_type invar1_value;
+      typedef typename Invariant2::result_type invar2_value;
+    
+      const Graph1& G1;
+      const Graph2& G2;
+      IsoMapping f;
+      Invariant1 invariant1;
+      Invariant2 invariant2;
+      std::size_t max_invariant;
+      IndexMap1 index_map1;
+      IndexMap2 index_map2;
+    
+      std::vector<vertex1_t> dfs_vertices;
+      typedef typename std::vector<vertex1_t>::iterator vertex_iter;
+      std::vector<int> dfs_num_vec;
+      typedef safe_iterator_property_map<typename std::vector<int>::iterator,
+                                         IndexMap1
+#ifdef BOOST_NO_STD_ITERATOR_TRAITS
+                                         , int, int&
+#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
+                                         > DFSNumMap;
+      DFSNumMap dfs_num;
+      std::vector<edge1_t> ordered_edges;
+      typedef typename std::vector<edge1_t>::iterator edge_iter;
+    
+      std::vector<char> in_S_vec;
+      typedef safe_iterator_property_map<typename std::vector<char>::iterator,
+                                         IndexMap2
+#ifdef BOOST_NO_STD_ITERATOR_TRAITS
+                                         , char, char&
+#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
+                                         > InSMap;
+      InSMap in_S;
+    
+      int num_edges_on_k;
+    
+      friend struct compare_multiplicity;
+      struct compare_multiplicity
+      {
+        compare_multiplicity(Invariant1 invariant1, size_type* multiplicity)
+          : invariant1(invariant1), multiplicity(multiplicity) { }
+        bool operator()(const vertex1_t& x, const vertex1_t& y) const {
+          return multiplicity[invariant1(x)] < multiplicity[invariant1(y)];
+        }
+        Invariant1 invariant1;
+        size_type* multiplicity;
+      };
+    
+      struct record_dfs_order : default_dfs_visitor
+      {
+        record_dfs_order(std::vector<vertex1_t>& v, std::vector<edge1_t>& e) 
+          : vertices(v), edges(e) { }
+    
+        void discover_vertex(vertex1_t v, const Graph1&) const {
+          vertices.push_back(v);
+        }
+        void examine_edge(edge1_t e, const Graph1&) const {
+          edges.push_back(e);
+        }
+        std::vector<vertex1_t>& vertices;
+        std::vector<edge1_t>& edges;
+      };
+    
+      struct edge_cmp {
+        edge_cmp(const Graph1& G1, DFSNumMap dfs_num)
+          : G1(G1), dfs_num(dfs_num) { }
+        bool operator()(const edge1_t& e1, const edge1_t& e2) const {
+          using namespace std;
+          int u1 = dfs_num[source(e1,G1)], v1 = dfs_num[target(e1,G1)];
+          int u2 = dfs_num[source(e2,G1)], v2 = dfs_num[target(e2,G1)];
+          int m1 = (max)(u1, v1);
+          int m2 = (max)(u2, v2);
+          // lexicographical comparison 
+          return std::make_pair(m1, std::make_pair(u1, v1))
+            < std::make_pair(m2, std::make_pair(u2, v2));
+        }
+        const Graph1& G1;
+        DFSNumMap dfs_num;
+      };
+    
+    public:
+      isomorphism_algo(const Graph1& G1, const Graph2& G2, IsoMapping f,
+                       Invariant1 invariant1, Invariant2 invariant2, std::size_t max_invariant,
+                       IndexMap1 index_map1, IndexMap2 index_map2)
+        : G1(G1), G2(G2), f(f), invariant1(invariant1), invariant2(invariant2),
+          max_invariant(max_invariant),
+          index_map1(index_map1), index_map2(index_map2)
+      {
+        in_S_vec.resize(num_vertices(G1));
+        in_S = make_safe_iterator_property_map
+          (in_S_vec.begin(), in_S_vec.size(), index_map2
+#ifdef BOOST_NO_STD_ITERATOR_TRAITS
+           , in_S_vec.front()
+#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
+           );
+      }
+    
+      bool test_isomorphism()
+      {
+        // reset isomapping
+        BGL_FORALL_VERTICES_T(v, G1, Graph1)
+          f[v] = graph_traits<Graph2>::null_vertex();
+          
+        {
+          std::vector<invar1_value> invar1_array;
+          BGL_FORALL_VERTICES_T(v, G1, Graph1)
+            invar1_array.push_back(invariant1(v));
+          sort(invar1_array);
+        
+          std::vector<invar2_value> invar2_array;
+          BGL_FORALL_VERTICES_T(v, G2, Graph2)
+            invar2_array.push_back(invariant2(v));
+          sort(invar2_array);
+          if (! equal(invar1_array, invar2_array))
+            return false;
+        }
+        
+        std::vector<vertex1_t> V_mult;
+        BGL_FORALL_VERTICES_T(v, G1, Graph1)
+          V_mult.push_back(v);
+        {
+          std::vector<size_type> multiplicity(max_invariant, 0);
+          BGL_FORALL_VERTICES_T(v, G1, Graph1)
+            ++multiplicity.at(invariant1(v));
+          sort(V_mult, compare_multiplicity(invariant1, &multiplicity[0]));
+        }
+        
+        std::vector<default_color_type> color_vec(num_vertices(G1));
+        safe_iterator_property_map<std::vector<default_color_type>::iterator,
+                                   IndexMap1
+#ifdef BOOST_NO_STD_ITERATOR_TRAITS
+                                   , default_color_type, default_color_type&
+#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
+                                   >
+          color_map(color_vec.begin(), color_vec.size(), index_map1);
+        record_dfs_order dfs_visitor(dfs_vertices, ordered_edges);
+        typedef color_traits<default_color_type> Color;
+        for (vertex_iter u = V_mult.begin(); u != V_mult.end(); ++u) {
+          if (color_map[*u] == Color::white()) {
+            dfs_visitor.start_vertex(*u, G1);
+            depth_first_visit(G1, *u, dfs_visitor, color_map);
+          }
+        }
+        // Create the dfs_num array and dfs_num_map
+        dfs_num_vec.resize(num_vertices(G1));
+        dfs_num = make_safe_iterator_property_map(dfs_num_vec.begin(),
+                                                  dfs_num_vec.size(), 
+                                                  index_map1
+#ifdef BOOST_NO_STD_ITERATOR_TRAITS
+                                                  , dfs_num_vec.front()
+#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
+                                                  );
+        size_type n = 0;
+        for (vertex_iter v = dfs_vertices.begin(); v != dfs_vertices.end(); ++v)
+          dfs_num[*v] = n++;
+        
+        sort(ordered_edges, edge_cmp(G1, dfs_num));
+        
+    
+        int dfs_num_k = -1;
+        return this->match(ordered_edges.begin(), dfs_num_k);
+      }
+    
+    private:
+      struct match_continuation {
+        enum {pos_G2_vertex_loop, pos_fi_adj_loop, pos_dfs_num} position;
+        typedef typename graph_traits<Graph2>::vertex_iterator vertex_iterator;
+        std::pair<vertex_iterator, vertex_iterator> G2_verts;
+        typedef typename graph_traits<Graph2>::adjacency_iterator adjacency_iterator;
+        std::pair<adjacency_iterator, adjacency_iterator> fi_adj;
+        edge_iter iter;
+        int dfs_num_k;
+      };
+
+      bool match(edge_iter iter, int dfs_num_k)
+      {
+        std::vector<match_continuation> k;
+        typedef typename graph_traits<Graph2>::vertex_iterator vertex_iterator;
+        std::pair<vertex_iterator, vertex_iterator> G2_verts(vertices(G2));
+        typedef typename graph_traits<Graph2>::adjacency_iterator adjacency_iterator;
+        std::pair<adjacency_iterator, adjacency_iterator> fi_adj;
+        vertex1_t i, j;
+
+        recur:
+        if (iter != ordered_edges.end()) {
+          i = source(*iter, G1);
+          j = target(*iter, G1);
+          if (dfs_num[i] > dfs_num_k) {
+            G2_verts = vertices(G2);
+            while (G2_verts.first != G2_verts.second) {
+              {
+                vertex2_t u = *G2_verts.first;
+                vertex1_t kp1 = dfs_vertices[dfs_num_k + 1];
+                if (invariant1(kp1) == invariant2(u) && in_S[u] == false) {
+                  {
+                    f[kp1] = u;
+                    in_S[u] = true;
+                    num_edges_on_k = 0;
+                    
+                    match_continuation new_k;
+                    new_k.position = match_continuation::pos_G2_vertex_loop;
+                    new_k.G2_verts = G2_verts;
+                    new_k.iter = iter;
+                    new_k.dfs_num_k = dfs_num_k;
+                    k.push_back(new_k);
+                    ++dfs_num_k;
+                    goto recur;
+                  }
+                }
+              }
+G2_loop_k:    ++G2_verts.first;
+            }
+               
+          }
+          else if (dfs_num[j] > dfs_num_k) {
+            {
+              vertex1_t vk = dfs_vertices[dfs_num_k];
+              num_edges_on_k -= 
+                count_if(adjacent_vertices(f[vk], G2), make_indirect_pmap(in_S));
+                  
+              for (int jj = 0; jj < dfs_num_k; ++jj) {
+                vertex1_t j = dfs_vertices[jj];
+                num_edges_on_k -= count(adjacent_vertices(f[j], G2), f[vk]);
+              }
+            }
+                
+            if (num_edges_on_k != 0)
+              goto return_point_false;
+            fi_adj = adjacent_vertices(f[i], G2);
+            while (fi_adj.first != fi_adj.second) {
+              {
+                vertex2_t v = *fi_adj.first;
+                if (invariant2(v) == invariant1(j) && in_S[v] == false) {
+                  f[j] = v;
+                  in_S[v] = true;
+                  num_edges_on_k = 1;
+                  BOOST_USING_STD_MAX();
+                  int next_k = max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num_k, max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num[i], dfs_num[j]));
+                  match_continuation new_k;
+                  new_k.position = match_continuation::pos_fi_adj_loop;
+                  new_k.fi_adj = fi_adj;
+                  new_k.iter = iter;
+                  new_k.dfs_num_k = dfs_num_k;
+                  ++iter;
+                  dfs_num_k = next_k;
+                  k.push_back(new_k);
+                  goto recur;
+                }
+              }
+fi_adj_loop_k:++fi_adj.first;
+            }
+          }
+          else {
+            if (container_contains(adjacent_vertices(f[i], G2), f[j])) {
+              ++num_edges_on_k;
+              match_continuation new_k;
+              new_k.position = match_continuation::pos_dfs_num;
+              k.push_back(new_k);
+              ++iter;
+              goto recur;
+            }
+                
+          }
+        } else 
+          goto return_point_true;
+        goto return_point_false;
+    
+        {
+          return_point_true: return true;
+
+          return_point_false:
+          if (k.empty()) return false;
+          const match_continuation& this_k = k.back();
+          switch (this_k.position) {
+            case match_continuation::pos_G2_vertex_loop: {G2_verts = this_k.G2_verts; iter = this_k.iter; dfs_num_k = this_k.dfs_num_k; k.pop_back(); in_S[*G2_verts.first] = false; i = source(*iter, G1); j = target(*iter, G1); goto G2_loop_k;}
+            case match_continuation::pos_fi_adj_loop: {fi_adj = this_k.fi_adj; iter = this_k.iter; dfs_num_k = this_k.dfs_num_k; k.pop_back(); in_S[*fi_adj.first] = false; i = source(*iter, G1); j = target(*iter, G1); goto fi_adj_loop_k;}
+            case match_continuation::pos_dfs_num: {k.pop_back(); goto return_point_false;}
+            default: {
+              BOOST_ASSERT(!"Bad position");
+#ifdef UNDER_CE
+              exit(-1);
+#else
+              abort();
+#endif
+            }
+          }
+        }
+      }
+    };
+
+    
+    template <typename Graph, typename InDegreeMap>
+    void compute_in_degree(const Graph& g, InDegreeMap in_degree_map)
+    {
+      BGL_FORALL_VERTICES_T(v, g, Graph)
+        put(in_degree_map, v, 0);
+
+      BGL_FORALL_VERTICES_T(u, g, Graph)
+        BGL_FORALL_ADJ_T(u, v, g, Graph)
+        put(in_degree_map, v, get(in_degree_map, v) + 1);
+    }
+
+  } // namespace detail
+
+
+  template <typename InDegreeMap, typename Graph>
+  class degree_vertex_invariant
+  {
+    typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
+    typedef typename graph_traits<Graph>::degree_size_type size_type;
+  public:
+    typedef vertex_t argument_type;
+    typedef size_type result_type;
+
+    degree_vertex_invariant(const InDegreeMap& in_degree_map, const Graph& g)
+      : m_in_degree_map(in_degree_map),
+        m_max_vertex_in_degree(0),
+        m_max_vertex_out_degree(0),
+        m_g(g) {
+      BGL_FORALL_VERTICES_T(v, g, Graph) {
+        m_max_vertex_in_degree =
+          (std::max)(m_max_vertex_in_degree, get(m_in_degree_map, v));
+        m_max_vertex_out_degree =
+          (std::max)(m_max_vertex_out_degree, out_degree(v, g));
+      }
+    }
+
+    size_type operator()(vertex_t v) const {
+      return (m_max_vertex_in_degree + 1) * out_degree(v, m_g)
+        + get(m_in_degree_map, v);
+    }
+    // The largest possible vertex invariant number
+    size_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const { 
+      return (m_max_vertex_in_degree + 1) * (m_max_vertex_out_degree + 1);
+    }
+  private:
+    InDegreeMap m_in_degree_map;
+    size_type m_max_vertex_in_degree;
+    size_type m_max_vertex_out_degree;
+    const Graph& m_g;
+  };
+
+  // Count actual number of vertices, even in filtered graphs.
+  template <typename Graph>
+  size_t count_vertices(const Graph& g)
+  {
+      size_t n = 0;
+      BGL_FORALL_VERTICES_T(v, g, Graph) {(void)v; ++n;}
+      return n;
+  }
+
+  template <typename Graph1, typename Graph2, typename IsoMapping, 
+    typename Invariant1, typename Invariant2,
+    typename IndexMap1, typename IndexMap2>
+  bool isomorphism(const Graph1& G1, const Graph2& G2, IsoMapping f, 
+                   Invariant1 invariant1, Invariant2 invariant2, 
+                   std::size_t max_invariant,
+                   IndexMap1 index_map1, IndexMap2 index_map2)
+
+  {
+    // Graph requirements
+    BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<Graph1> ));
+    BOOST_CONCEPT_ASSERT(( EdgeListGraphConcept<Graph1> ));
+    BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<Graph2> ));
+    //BOOST_CONCEPT_ASSERT(( BidirectionalGraphConcept<Graph2> ));
+    
+    typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;
+    typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
+    typedef typename graph_traits<Graph1>::vertices_size_type size_type;
+    
+    // Vertex invariant requirement
+    BOOST_CONCEPT_ASSERT(( AdaptableUnaryFunctionConcept<Invariant1,
+      size_type, vertex1_t> ));
+    BOOST_CONCEPT_ASSERT(( AdaptableUnaryFunctionConcept<Invariant2,
+      size_type, vertex2_t> ));
+    
+    // Property map requirements
+    BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<IsoMapping, vertex1_t> ));
+    typedef typename property_traits<IsoMapping>::value_type IsoMappingValue;
+    BOOST_STATIC_ASSERT((is_convertible<IsoMappingValue, vertex2_t>::value));
+    
+    BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<IndexMap1, vertex1_t> ));
+    typedef typename property_traits<IndexMap1>::value_type IndexMap1Value;
+    BOOST_STATIC_ASSERT((is_convertible<IndexMap1Value, size_type>::value));
+    
+    BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<IndexMap2, vertex2_t> ));
+    typedef typename property_traits<IndexMap2>::value_type IndexMap2Value;
+    BOOST_STATIC_ASSERT((is_convertible<IndexMap2Value, size_type>::value));
+    
+    if (count_vertices(G1) != count_vertices(G2))
+      return false;
+    if (count_vertices(G1) == 0 && count_vertices(G2) == 0)
+      return true;
+    
+    detail::isomorphism_algo<Graph1, Graph2, IsoMapping, Invariant1,
+      Invariant2, IndexMap1, IndexMap2> 
+      algo(G1, G2, f, invariant1, invariant2, max_invariant, 
+           index_map1, index_map2);
+    return algo.test_isomorphism();
+  }
+
+
+  namespace detail {
+  
+    template <typename Graph1, typename Graph2, 
+      typename IsoMapping, 
+      typename IndexMap1, typename IndexMap2,
+      typename P, typename T, typename R>
+    bool isomorphism_impl(const Graph1& G1, const Graph2& G2, 
+                          IsoMapping f, IndexMap1 index_map1, IndexMap2 index_map2,
+                          const bgl_named_params<P,T,R>& params)
+    {
+      std::vector<std::size_t> in_degree1_vec(num_vertices(G1));
+      typedef safe_iterator_property_map<std::vector<std::size_t>::iterator,
+                                         IndexMap1
+#ifdef BOOST_NO_STD_ITERATOR_TRAITS
+                                         , std::size_t, std::size_t&
+#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
+                                         > InDeg1;
+      InDeg1 in_degree1(in_degree1_vec.begin(), in_degree1_vec.size(), index_map1);
+      compute_in_degree(G1, in_degree1);
+
+      std::vector<std::size_t> in_degree2_vec(num_vertices(G2));
+      typedef safe_iterator_property_map<std::vector<std::size_t>::iterator, 
+                                         IndexMap2
+#ifdef BOOST_NO_STD_ITERATOR_TRAITS
+                                         , std::size_t, std::size_t&
+#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
+                                         > InDeg2;
+      InDeg2 in_degree2(in_degree2_vec.begin(), in_degree2_vec.size(), index_map2);
+      compute_in_degree(G2, in_degree2);
+
+      degree_vertex_invariant<InDeg1, Graph1> invariant1(in_degree1, G1);
+      degree_vertex_invariant<InDeg2, Graph2> invariant2(in_degree2, G2);
+
+      return isomorphism(G1, G2, f,
+                         choose_param(get_param(params, vertex_invariant1_t()), invariant1),
+                         choose_param(get_param(params, vertex_invariant2_t()), invariant2),
+                         choose_param(get_param(params, vertex_max_invariant_t()), (invariant2.max)()),
+                         index_map1, index_map2
+                         );  
+    }  
+
+    template <typename G, typename Index>
+    struct make_degree_invariant {
+      const G& g;
+      const Index& index;
+      make_degree_invariant(const G& g, const Index& index): g(g), index(index) {}
+      typedef typename boost::graph_traits<G>::degree_size_type degree_size_type;
+      typedef shared_array_property_map<degree_size_type, Index> prop_map_type;
+      typedef degree_vertex_invariant<prop_map_type, G> result_type;
+      result_type operator()() const {
+        prop_map_type pm = make_shared_array_property_map(num_vertices(g), degree_size_type(), index);
+        compute_in_degree(g, pm);
+        return result_type(pm, g);
+      }
+    };
+   
+  } // namespace detail
+
+  namespace graph {
+    namespace detail {
+      template <typename Graph1, typename Graph2>
+      struct isomorphism_impl {
+        typedef bool result_type;
+        template <typename ArgPack>
+        bool operator()(const Graph1& g1, const Graph2& g2, const ArgPack& arg_pack) const {
+          using namespace boost::graph::keywords;
+          typedef typename boost::detail::override_const_property_result<ArgPack, tag::vertex_index1_map, boost::vertex_index_t, Graph1>::type index1_map_type;
+          typedef typename boost::detail::override_const_property_result<ArgPack, tag::vertex_index2_map, boost::vertex_index_t, Graph2>::type index2_map_type;
+          index1_map_type index1_map = boost::detail::override_const_property(arg_pack, _vertex_index1_map, g1, boost::vertex_index);
+          index2_map_type index2_map = boost::detail::override_const_property(arg_pack, _vertex_index2_map, g2, boost::vertex_index);
+          typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
+          typename std::vector<vertex2_t>::size_type n = (typename std::vector<vertex2_t>::size_type)num_vertices(g1);
+          std::vector<vertex2_t> f(n);
+          typename boost::parameter::lazy_binding<
+                     ArgPack,
+                     tag::vertex_invariant1,
+                     boost::detail::make_degree_invariant<Graph1, index1_map_type> >::type
+            invariant1 =
+              arg_pack[_vertex_invariant1 || boost::detail::make_degree_invariant<Graph1, index1_map_type>(g1, index1_map)];
+          typename boost::parameter::lazy_binding<
+                     ArgPack,
+                     tag::vertex_invariant2,
+                     boost::detail::make_degree_invariant<Graph2, index2_map_type> >::type
+            invariant2 =
+              arg_pack[_vertex_invariant2 || boost::detail::make_degree_invariant<Graph2, index2_map_type>(g2, index2_map)];
+          return boost::isomorphism
+                   (g1, g2,
+                    choose_param(arg_pack[_isomorphism_map | boost::param_not_found()],
+                                 make_shared_array_property_map(num_vertices(g1), vertex2_t(), index1_map)),
+                    invariant1,
+                    invariant2,
+                    arg_pack[_vertex_max_invariant | (invariant2.max)()],
+                    index1_map,
+                    index2_map);
+        }
+      };
+    }
+    BOOST_GRAPH_MAKE_FORWARDING_FUNCTION(isomorphism, 2, 6)
+  }
+
+  // Named parameter interface
+  BOOST_GRAPH_MAKE_OLD_STYLE_PARAMETER_FUNCTION(isomorphism, 2)
+
+  // Verify that the given mapping iso_map from the vertices of g1 to the
+  // vertices of g2 describes an isomorphism.
+  // Note: this could be made much faster by specializing based on the graph
+  // concepts modeled, but since we're verifying an O(n^(lg n)) algorithm,
+  // O(n^4) won't hurt us.
+  template<typename Graph1, typename Graph2, typename IsoMap>
+  inline bool verify_isomorphism(const Graph1& g1, const Graph2& g2, IsoMap iso_map)
+  {
+#if 0
+    // problematic for filtered_graph!
+    if (num_vertices(g1) != num_vertices(g2) || num_edges(g1) != num_edges(g2))
+      return false;
+#endif
+  
+    BGL_FORALL_EDGES_T(e1, g1, Graph1) {
+      bool found_edge = false;
+      BGL_FORALL_EDGES_T(e2, g2, Graph2) {
+        if (source(e2, g2) == get(iso_map, source(e1, g1)) &&
+            target(e2, g2) == get(iso_map, target(e1, g1))) {
+          found_edge = true;
+        }
+      }
+    
+      if (!found_edge)
+        return false;
+    }
+  
+    return true;
+  }
+
+} // namespace boost
+
+#ifdef BOOST_ISO_INCLUDED_ITER_MACROS
+#undef BOOST_ISO_INCLUDED_ITER_MACROS
+#include <boost/graph/iteration_macros_undef.hpp>
+#endif
+
+#endif // BOOST_GRAPH_ISOMORPHISM_HPP